Mathematics

In parallelogram $$ABCD$$ two points $$P$$ and $$Q$$ are taken on diagonal $$BD$$ such that $$DP=BQ (see fig. 8.20)$$. 
Show that:  $$AP = CQ$$ 


SOLUTION
Given $$ABCD$$ is parallelogram and given $$BD$$ is diagonal such that 

$$DP= BQ$$

$$\Rightarrow $$ Now $$AD \parallel BC$$ [$$AD$$ is parallel to $$BC$$]

$$BD$$ is transversal i.e., diagonal 

In $$\triangle APD$$ & $$\triangle CQB$$

$$AD= CB$$

$$\angle ADP= \angle CBQ $$  [Diagonals bisect the angles ]

$$DP= BQ$$

$$\therefore \triangle APD \cong \triangle CQB$$ [$$SAS$$ concurrency ]

$$\therefore AP= CQ$$
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Subjective Medium Published on 09th 09, 2020
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